Which of the following numbers is a multiple of 7? ${44,57,94,105,108}$
Solution: The multiples of $7$ are $7$ $14$ $21$ $28$ ..... In general, any number that leaves no remainder when divided by $7$ is considered a multiple of $7$ We can start by dividing each of our answer choices by $7$ $44 \div 7 = 6\text{ R }2$ $57 \div 7 = 8\text{ R }1$ $94 \div 7 = 13\text{ R }3$ $105 \div 7 = 15$ $108 \div 7 = 15\text{ R }3$ The only answer choice that leaves no remainder after the division is $105$ $ 15$ $7$ $105$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $105$ $105 = 3\times5\times7 7 = 7$ Therefore the only multiple of $7$ out of our choices is $105$. We can say that $105$ is divisible by $7$.